The diagnosability is one of the most important measures of the reliability of networks. Consider the setting where there are large-scale failures that disconnect the network and result in many components. Then, the diagnosability is closely related to the number of components. In this paper, we define and study the $\boldsymbol{g}$-component diagnosability of network $\boldsymbol{G}$, which is denoted by $\boldsymbol{ct_g(G)}$ and has not been addressed before. $\boldsymbol{ct_g(G)}$ is the maximum number of nodes in the faulty node set $\boldsymbol{F}$ of $\boldsymbol{G}$ such that $\boldsymbol{G-F}$ has at least $\boldsymbol{g}$ components and diagnosis model can identify all nodes in $\boldsymbol{F}$. Under PMC and MM$^*$ diagnosis models, we show that, in the hypercube $\boldsymbol{Q_n\ (n\geq 7)}$, $\boldsymbol{ct_{g+1}(Q_n)=-(1/2)g^2+(n-3/2)g+n}$ when $\boldsymbol{g\leq n-1}$. Moreover, we determine the $\boldsymbol{(n+1)}$-component diagnosability $\boldsymbol{ct_{n+1}(Q_n)=n^2/2+n/2-2}$ for $\boldsymbol{n\geq 7}$.

The present paper proposes a neural network-based adaptive region-tracking control strategy for a flexible-joint robot manipulator subjected to region constraints. The developed neural network-based control strategy can globally stabilize the robot manipulator and cope with model uncertainties and the external unknown bounded disturbances. Different from the existing literature, by using the sliding mode technology and the singular perturbation theory, the developed control strategy does not require the high-order derivatives of the link states such as jerk and acceleration since the high-order derivative information is not always available in practical applications. By using Lyapunov stability theory, it is proved that the proposed neural network-based control strategy can guarantee that all the parameter variables in the closed-loop system are bounded, and the flexible-joint robot manipulator with unknown dynamics can reach inside the dynamic region and also maintain the velocity matching with the desired moving region. Since the assumption of linearization of the unknown dynamic parameters is removed, the proposed control strategy does not require the calculation of the complex regression matrix. Therefore, the proposed method has great robustness and the ability of model generalization. Simulations are given to demonstrate the validity of the proposed control strategy.

The non-synchronous measurement (NSM) technology has been significantly developed. NSM at the coprime position (CP-NSM) is a measurement principle in two-dimensional (2D) acoustic imaging, wherein a planar array is moved to a coprime position for measurements. However, there are certain drawbacks to the measurement principles of spherical arrays in three-dimensional (3D) acoustic imaging. A measurement principle of 3D acoustic imaging has been investigated using 3D Non-Synchronous Measurements with a Central Reference based on Revolution and Autorotation (CR-NSM). The primary contributions of this CR-NSM are as follows: (1) A measurement principle for 3D non-synchronous measurements with a central reference based on revolution and autorotation is proposed. (2) The spatial resolution is primarily determined by the revolution in CR-NSM, and the side lobe is reduced by autorotation in CR-NSM. In the simulation results, the spatial resolution is obtained using CR-NSM for good imaging at low signal-to-noise ratios (SNR). Moreover, the cross-spectral matrix (CSM) completion error is enhanced by adding the phase relations between consecutive positions. The CR-NSM algorithm was developed according to the measurement principles of 3D acoustic imaging.

Rotating source beamforming techniques have been effective means of noise localization on rotary machines. In this letter, we derive an alternative expression for modal composition beamforming (MCB) and subsequently consider the equivalent source assumption and cyclostationarity of the constant angular-speed rotating sound source so that a rotating sound source power (RSP) propagation model is derived. By estimating a suitable solution for the RSP model using the subspace variational Bayesian (SVB) technique with sparsity and total variation (TV) priors, the validity of the RSP model was established. According to the simulation results, the proposed RSP-SVB method leads to a significantly higher resolution than the MCB method. It can localize multiple fast-rotating sound sources accurately, rapidly, and effectively in environments with strong background noise interference. Therefore, our proposed RSP-SVB can offer a reliable solution for identifying fast-rotating blade noise.